1. Field of the Invention
This invention relates generally to active control of sound, vibration or other physical phenomena. More particularly, this invention relates to increasing the computational efficiency of active control of sound or vibration by reducing a sampling rate and reducing a control rate.
2. Background
Conventional active control systems consist of a number of sensors that measure the ambient variables of interest (e.g. sound or vibration), a number of actuators capable of generating an effect on these variables (e.g. by producing sound or vibration), and a computer which processes the information received from the sensors and sends commands to the actuators so as to reduce the amplitude of the sensor signals. The control algorithm is the scheme by which the decisions are made as to what commands to the actuators are appropriate.
Many relevant sound/vibration problems are tonal in nature, that is, the variable of interest has information predominantly at relatively few distinct frequencies (or within a narrow bandwidth about these frequencies). Such is the case, for example, where rotating machinery causes the noise or vibration. One key problem, particularly for higher frequency applications, is the computational burden required to directly implement active control solutions using existing approaches. In typical control systems, the amount of computation required for the control algorithm is proportional to the frequency of the noise or vibration.
Most active control approaches use digital signal processors (DSP's) and require sampling of the signals from the sensor or sensors of interest (microphones and/or accelerometers in the current application). Typically, the sampling frequency, fs, is at least twice, and usually roughly three times the highest frequency of interest. This is to prevent aliasing, and follows from the Nyquist criterion. The Nyquist criterion or sampling theorem states that for a sample rate fs, information in any frequency band between (2n−1)*fs/2 and (2n+1)*fs/2 for integer n aliases to the band of interest from −fs/2 to fs/2. Thus for a frequency of interest fd, information on the sensor signals at any of the frequencies |fd±nfs| for n=1, 2, 3, . . . will be indistinguishable from the desired information at fd and will result in degraded control performance. To avoid this aliasing “noise”, anti-alias low-pass filters are used with a corner frequency fc larger than fd and smaller than fs so that the filter attenuates information at frequency fs−fd sufficiently to avoid a significant loss in performance.
Similarly, if the DSP outputs at a frequency fs a signal of frequency fd then there are additional tones generated at frequencies |fd±nfs| for integer n. Low-pass reconstruction filters are required to smooth the actuator command signals so that only the desired frequency component has significant energy content.
Once the sensor data is within the DSP, all of the computations related to the control algorithm are typically performed at the same sample rate fs, and the resulting control signals are output to the actuators at the same sample rate. For a tonal problem at frequency fd, a sensor signal yk in the computer at time tk can be written asyk=ak cos(fdtk)+bk sin(fdtk)+wkwhere wk is the background noise, and ak and bk represent the information about the tone. One possible way to perform the control computation for a tonal problem is as follows. First, the sensor signal(s) are multiplied by reference sine and cosine signals at the frequency of interest. For most tonal applications, this disturbance frequency can be easily obtained from suitable reference sensors. This demodulation process is one of several methods for obtaining estimates of the time-varying variables ak and bk above. The resulting signals are passed through a gain matrix (2×2 for a single sensor and actuator, or 2na×2ns for a problem with na actuators and ns sensors). For a large number of sensors and actuators, the matrix multiplication involved is computationally expensive. After passing through a low pass filter, the signals are again multiplied by the same reference sine and cosine terms and added to form the output. It can be shown that this process results in excellent disturbance rejection at the frequency of the reference signals, and is similar to many other tonal control approaches. The gain matrix and the frequency of the low pass filter determine the magnitude and phase of the compensator in the neighborhood of the reference frequency. The process can be extended to any number of tones.